Geodesic
On regular Stein neighborhoods of a union of two totally real planes in $\mathbb {C}^2$
Tadej Starčič1
1 Faculty of Education University of Ljubljana Kardeljeva Ploščad 16 1000 Ljubljana, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska 19 1000 Ljubljana, Slovenia
Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 1-15.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We find regular Stein neighborhoods of a union of totally real planes $M=(A+iI)\mathbb {R}^2$ and $N=\mathbb {R}^2$ in $\mathbb {C}^2$, provided that the entries of a real $2 \times 2$ matrix $A$ are sufficiently small. A key step in our proof is a local construction of a suitable function $\rho $ near the origin. The sublevel sets of $\rho $ are strongly Levi pseudoconvex and admit strong deformation retraction to $M\cup N$.
DOI : 10.4064/ap3754-4-2016
Keywords: regular stein neighborhoods union totally real planes mathbb mathbb mathbb provided entries real times matrix sufficiently small key step proof local construction suitable function rho near origin sublevel sets rho strongly levi pseudoconvex admit strong deformation retraction cup

Tadej Starčič 1

1 Faculty of Education University of Ljubljana Kardeljeva Ploščad 16 1000 Ljubljana, Slovenia and Institute of Mathematics, Physics and Mechanics Jadranska 19 1000 Ljubljana, Slovenia 
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Tadej Starčič. On regular Stein neighborhoods of a union of two totally real planes in $\mathbb {C}^2$. Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 1-15. doi : 10.4064/ap3754-4-2016. http://geodesic.mathdoc.fr/articles/10.4064/ap3754-4-2016/

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